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Progress in noncommutative function theory
Journal article   Peer reviewed

Progress in noncommutative function theory

Paul Muhly and Baruch Solel
Science China. Mathematics, Vol.54(11), pp.2275-2294
11/2011
DOI: 10.1007/s11425-011-4241-6
url
https://arxiv.org/pdf/1008.4069View
Open Access

Abstract

In this expository paper, we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.
46L08 Schur class Mathematics representations 47L30 46L52 47L75 Hardy algebras tensor algebras W -correspondence Applications of Mathematics 46L89 47L65 47L55

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